Curing basis-set convergence of wave-function theory using density-functional theory: a systematically improvable approach

The present work proposes to use density-functional theory (DFT) to correct for the basis-set error of wave-function theory (WFT). One of the key ideas developed here is to define a range-separation parameter which automatically adapts to a given basis set. The derivation of the exact equations are based on the Levy-Lieb formulation of DFT, which helps us to define a complementary functional which corrects uniquely for the basis-set error of WFT. The coupling of DFT and WFT is done through the definition of a real-space representation of the electron-electron Coulomb operator projected in a one-particle basis set. Such an effective interaction has the particularity to coincide with the exact electron-electron interaction in the limit of a complete basis set, and to be finite at the electron-electron coalescence point when the basis set is incomplete. The non-diverging character of the effective interaction allows one to define a mapping with the long-range interaction used in the context of range-separated DFT and to design practical approximations for the unknown complementary functional. Here, a local-density approximation is proposed for both full-configuration-interaction (FCI) and selected configuration-interaction approaches. Our theory is numerically tested to compute total energies and ionization potentials for a series of atomic systems. The results clearly show that the DFT correction drastically improves the basis-set convergence of both the total energies and the energy differences. For instance, a sub kcal/mol accuracy is obtained from the aug-cc-pVTZ basis set with the method proposed here when an aug-cc-pV5Z basis set barely reaches such a level of accuracy at the near FCI level

Preuilly – Le Bourg

Date de l'opération : 1984 - 1985 (SU) Inventeur(s) : La Ferté M Dans un terrain situé au nord-est de l'église paroissiale et à proximité immédiate du Cher, des thermes appartenant à une grande villa ont été partiellement fouillés. Succédant à une construction de nature indéterminée, représentée par deux tronçons de murs distants de 0,85 m, les huit pièces mises au jour appartiennent à deux états distincts, dont le premier compte au moins cinq pièces dont trois piscines de plan circulaire et ..

Pilotage du chargement en formulation X-FEM: application aux lois cohésives

National audienceSee http://hal.archives-ouvertes.fr/docs/00/59/28/21/ANNEX/r_22HF3P0A.pd

More Than 1700 Years of Word Equations

Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical study of word equations began only in the 20th century. So, the title of the present article does not seem to be justified at all. However, a linear Diophantine equation can be viewed as a special case of a system of word equations over a unary alphabet, and, more importantly, a word equation can be viewed as a special case of a Diophantine equation. Hence, the problem WordEquations: "Is a given word equation solvable?" is intimately related to Hilbert's 10th problem on the solvability of Diophantine equations. This became clear to the Russian school of mathematics at the latest in the mid 1960s, after which a systematic study of that relation began. Here, we review some recent developments which led to an amazingly simple decision procedure for WordEquations, and to the description of the set of all solutions as an EDT0L language.Comment: The paper will appear as an invited address in the LNCS proceedings of CAI 2015, Stuttgart, Germany, September 1 - 4, 201

Clusters in the critical branching Brownian motion

Brownian particles that are replicated and annihilated at equal rate have strongly correlated positions, forming a few compact clusters separated by large gaps. We characterize the distribution of the particles at a given time, using a definition of clusters in terms a coarse-graining length recently introduced by some of us. We show that, in a non-extinct realization, the average number of clusters grows as $\sim t^{D_{\mathrm{f}}/2}$ where $D_{\mathrm{f}} \approx 0.22$ is the Haussdoff dimension of the boundary of the super-Brownian motion, found by Mueller, Mytnik, and Perkins. We also compute the distribution of gaps between consecutive particles. We find two regimes separated by the characteristic length scale $\ell = \sqrt{D/\beta}$ where $D$ is the diffusion constant and $\beta$ the branching rate. The average number of gaps greater than $g$ decays as $\sim g^{D_{\mathrm{f}}-2}$ for $g\ll \ell$ and $\sim g^{-D_{\mathrm{f}}}$ for $g \gg \ell$. Finally, conditioned on the number of particles $n$, the above distributions are valid for $g \ll \sqrt{n}$; the average number of gaps greater than $g \gg \sqrt{n}$ is much less than one, and decays as $\simeq 4 (g/\sqrt{n})^{-2}$, in agreement with the universal gap distribution predicted by Ramola, Majumdar, and Schehr. Our results interpolate between a dense super-Brownian motion regime and a large-gap regime, unifying two previously independent approaches.Comment: 20 pages, 9 figure

La représentation de l'harmonie à travers la mélodie pour une improvisation jazz au saxophone sans accompagnement

La présente thèse porte sur l’improvisation jazz, et plus particulièrement sur sa pratique sans accompagnement au saxophone. Cette pratique est efficace surtout pour les musiciens qui jouent des instruments monodiques, comme le saxophone. L’objectif est d’analyser la compétence de certains saxophonistes en ce qui concerne surtout l’habileté de bien utiliser mélodiquement le contenu harmonique présent dans l’ensemble des standards qui font partie intégrante du répertoire jazz. La démarche de recherche adoptée est constituée, dans un premier temps, d’une recherche de plusieurs points de vue chez différents musiciens de jazz reconnus mondialement qui ont intégré la pratique sans accompagnement systématiquement dans leur routine. Dans un deuxième temps, des transcriptions d’extraits d’improvisations sans accompagnement ont été réalisées, avec un approfondissement quant à la pratique du saxophoniste Chris Potter. Ces transcriptions, qui ont été faites au saxophone ténor (donc sur un instrument transpositeur en si bémol), ont été analysées théoriquement afin d’identifier la manière dont le saxophoniste intègre le concept d’improvisation harmonique. Après ces analyses théoriques, l’auteur présente son point de vue concernant les moyens utilisés par Chris Potter pour faire ressortir l’harmonie à travers la mélodie improvisée. L’étape suivante a consisté à l’appropriation des moyens liés à la pratique sans accompagnement en tant que saxophoniste, permettant de mieux intégrer les aspects harmoniques des standards étudiés pour améliorer la qualité des improvisations lors du jeu en groupe. Finalement, les résultats obtenus permettent d’observer que la pratique de l’improvisation jazz sans accompagnement à travers le concept d’improvisation harmonique améliore la performance dans une situation réelle de concert

Urate Oxidase Purification by Salting-in Crystallization : Towards an Alternative to Chromatography

Background: Rasburicase (FasturtecH or ElitekH, Sanofi-Aventis), the recombinant form of urate oxidase from Aspergillus flavus, is a therapeutic enzyme used to prevent or decrease the high levels of uric acid in blood that can occur as a result of chemotherapy. It is produced by Sanofi-Aventis and currently purified via several standard steps of chromatography. This work explores the feasibility of replacing one or more chromatography steps in the downstream process by a crystallization step. It compares the efficacy of two crystallization techniques that have proven successful on pure urate oxidase, testing them on impure urate oxidase solutions